The aim of this paper is to present best proximity point results of (α -η;ψ)- proximal mappings satisfying local contractive conditions on a closed ball in the framework of complete metric spaces. An example is also presented to validate the result proved herein. As an application of our results, we prove existence of best proximity points of locally contractive mappings in the frame work of metric spaces endowed with binary relation. Our results extend and generalize various comparable results in the existing literature.